Problem: Simplify the following expression: $a = \dfrac{11}{-99k + 110}$ You can assume $k \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $11 = (11)$ The denominator can be factored: $-99k + 110 = - (3\cdot3\cdot11 \cdot k) + (2\cdot5\cdot11)$ The greatest common factor of all the terms is $11$ Factoring out $11$ gives us: $a = \dfrac{(11)(1)}{(11)(-9k + 10)}$ Dividing both the numerator and denominator by $11$ gives: $a = \dfrac{1}{-9k + 10}$